Setting up multiple domains

I have a Dutch website and thinking about translating part of it to English. However, my current domain is in Dutch, so I registered a more international domain as well. I’m having a hard time configuring this new domain.

I want this:
Dutch visitors go to website.nl
English visitors go to website.com

But no matter what I try, when I visit website.com I always end up at website.nl. Both domains are part of the same hosting package and both direct to the rootmap of my webspace. I tried Polylang (the plugin I wanted to use anyway to translate) and set both domains as Dutch and English languages, with the same result. I tried the plugin ‘Multiple Domain’, also no result… am I missing something that is really obvious? Can’t seem to find decent guides as well, but maybe I’m just looking in the wrong places. Any word of advise?